Electric Potential II

1
Electric Potential II

• We continue with finding the potential for a
  variety of charge configuration and look a the
  special properties of conductors.

2
Formulas for Electric Potential

• If the electric field is uniform
• If there is a point charge
• The constant is usually taken to be zero at
  infinity.

3
Principle of Superposition

• If we have more than one point charge, we just
  add the potentials at the desired point due to
  the individual charges.
• This is a scalar sum!
• The qi are the source charges.
• The signs of the qi matter!

4
Energy

• How much work (energy) does it take to bring a
  charge q0 to the point P?
• U q0V
• This is NOT the total energy stored in the
  system.
• We have to assemble the charges one at a time.

5
Energy II

• Bring in the first charge.
• No work is required.

• Bring in the 2nd charge.
• This requires work.

• Bring in the 4th charge.

• Bring in the 3rd charge.
• This requires work.

6
Electric Field from Electric Potential

• Integration and Differentiation are inverse
  operation.
• One undoes the other.
• Since V is the integral of E, then E is the
  derivative of V.
• We can see this in one dimension most easily.

7
Potential due to a line of charge

• Find the potential at the origin.

8
V inside outside an insulating sphere
9
Properties of Charged Conductors

• Every point on the surface of a charged conductor
  in equilibrium is at the same electric potential.
• E is normal to the surface.
• The electric potential inside a conductor is
  constant and equal to that at the surface.
• E is zero inside a conductor.

10
Potential of Conducting Shell
11
Two conductors connected by a wire

• Both conductors (and the wire) have the same
  potential at their surfaces.
• The electric fields are different.